A Mañé-Manning formula for expanding measures for endomorphisms of ${\mathbb{P}}^k$

Fabrizio Bianchi, Yan Mary He

Let $k\ge 1$ be an integer and $f$ a holomorphic endomorphism of ${\mathbb{P}}^k(\mathbb{C})$ of algebraic degree $d\ge 2$. We introduce a volume dimension for ergodic $f$-invariant…